Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
380 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11718740 | C2 | semidirect |
| 4. #11718739 | C2 | semidirect |
| 5. #11718726 | C2 | semidirect |
| 54. #6099 | Q8 | semidirect |
| 75. #1055 | C2×Q8 | semidirect |
| 148. C13 | #3165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#533 | 2 |
| C2×#88123 | 2 |
| #11718740 | 2 |
| #11718739 | 2 |
| #11718726 | 2 |
| #11718656 | 2 |
| C4×#6099 | 2 |
| #3165 | 13 |